# Distributions of full and non-full words in beta-expansions

## TL;DR

This paper characterizes the structure of full and non-full words in beta-expansions, providing precise lengths of maximal runs among admissible words with the same order.

## Contribution

It offers a complete characterization of full and non-full words in beta-expansions, including exact lengths of maximal runs, advancing understanding of their combinatorial structure.

## Key findings

- Complete characterization of full and non-full words in beta-expansions
- Precise lengths of maximal runs among admissible words
- Structural insights into beta-expansion word distributions

## Abstract

The structures of full words and non-full for $\beta$-expansions are completely characterized in this paper. We obtain the precise lengths of all the maximal runs of full and non-full words among admissible words with same order.